Translation:The team is let down by their best player.
Shouldn't it be, "The team is let down by its best player" ? I say this because of the verb "is".
That translation is incorrect following American usage; in American English, team is singular. Is it plural in British? It obviously is in Danish. In any case, both "its" and "their" should be accepted as correct.
No, I think it's singular in any version of English, and in any other language. It's just a common mistake that's often made. It should be both "sin" and "its" here.
The term for this in Eglish is collective nouns, they can be used as singular or plural depending on context (and from what I've read I'd say that here it should be singular). I haven't looked into it that much, but some sources claim that singular use is more common in AmE while plural in BrE.
That's right. In British English we very frequently use a singular noun together with a plural verb when referring to sports teams, for example: England have lost to Iceland; The England football team are useless; Team GB have won lots of Olympic medals.
(French speaker) Sure, but you can't change grammatical number in the midst of the sentence. It's either "The team is let down by its best players" or "The team are let down by their best players". Not mix of both.